IDEAS home Printed from https://ideas.repec.org/a/inm/orijoc/v36y2024i6p1481-1500.html
   My bibliography  Save this article

A FAST Method for Nested Estimation

Author

Listed:
  • Guo Liang

    (Institute of Statistics and Big Data, Renmin University of China, Beijing 100872, China)

  • Kun Zhang

    (Institute of Statistics and Big Data, Renmin University of China, Beijing 100872, China)

  • Jun Luo

    (Antai College of Economics and Management, Shanghai Jiao Tong University, Shanghai 200240, China)

Abstract

Nested estimation involves estimating an expectation of a function of a conditional expectation and has many important applications in operations research and machine learning. Nested simulation is a classic approach to this estimation, and the convergence rate of the mean squared error (MSE) of nested simulation estimators is only of order Γ − 2 / 3 , where Γ is the simulation budget. To accelerate the convergence, in this paper, we establish a jackkniFe-bAsed neSted simulaTion (FAST) method for nested estimation, and a unified theoretical analysis for general functions in the nested estimation shows that the MSE of the proposed method converges at the faster rate of Γ − 4 / 5 or even Γ − 6 / 7 . We also provide an efficient algorithm that ensures the estimator’s MSE decays at its optimal rate in practice. In numerical experiments, we apply the proposed estimator in portfolio risk measurement and Bayesian experimental design in operations research and machine learning areas, respectively, and numerical results are consistent with the theory presented.

Suggested Citation

  • Guo Liang & Kun Zhang & Jun Luo, 2024. "A FAST Method for Nested Estimation," INFORMS Journal on Computing, INFORMS, vol. 36(6), pages 1481-1500, December.
    • Handle: RePEc:inm:orijoc:v:36:y:2024:i:6:p:1481-1500
    DOI: 10.1287/ijoc.2023.0118
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/ijoc.2023.0118
    Download Restriction: no
    File URL: https://libkey.io/10.1287/ijoc.2023.0118?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:orijoc:v:36:y:2024:i:6:p:1481-1500. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.